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December 1997 On nonparametric confidence intervals
Mark G. Low
Ann. Statist. 25(6): 2547-2554 (December 1997). DOI: 10.1214/aos/1030741084


An inequality is given for the expected length of a confidence interval given that a particular distribution generated the data and assuming that the confidence interval has a given coverage probability over a family of distributions. As a corollary, attempts to adapt to the regularity of the true density within derivative smoothness classes cannot improve the rate of convergence of the length of the confidence interval over minimax fixed-length intervals and still maintain uniform coverage probability. However, adaptive confidence intervals can attain improved rates of convergence in some other classes of densities, such as those satisfying a shape restriction.


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Mark G. Low. "On nonparametric confidence intervals." Ann. Statist. 25 (6) 2547 - 2554, December 1997.


Published: December 1997
First available in Project Euclid: 30 August 2002

zbMATH: 0894.62055
MathSciNet: MR1604412
Digital Object Identifier: 10.1214/aos/1030741084

Primary: 62G07

Keywords: confidence intervals , Density estimation

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 6 • December 1997
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